A129867 Row sums of triangular array T: T(j,k) = k*(j-k)! for k < j, T(j,k) = 1 for k = j; 1 <= k <= j.

1, 2, 5, 14, 47, 200, 1073, 6986, 53219, 462332, 4500245, 48454958, 571411271, 7321388384, 101249656697, 1502852293010, 23827244817323, 401839065437636, 7182224591785949, 135607710526966262, 2696935204638786575

Offset: 1

Author

Paul Curtz, May 24 2007

Keywords

• nonn

Comments

T read by rows is in A130469.

First differences are 1, 3, 9, 33, 153, 873, 5913, ... (see A007489), second differences are 2, 6, 24, 120, 720, 5040, ... (see A000142 ).

First terms of the sequences of m-th differences are 1, 2, 4, 14, 64, ... (see A055790, A047920, A068106).

Antidiagonal sums are 1, 1, 3, 8, 29, 135, ... (see A130470) with first differences 0, 2, 5, 21, 106, ... (see A130471).

Equals the row sums of irregular triangle A182961. - Paul D. Hanna, Mar 05 2012

Examples

			First seven rows of T are
[   1 ]
[   1,   1 ]
[   2,   2,   1 ]
[   6,   4,   3,   1 ]
[  24,  12,   6,   4,   1 ]
[ 120,  48,  18,   8,   5,   1 ]
[ 720, 240,  72,  24,  10,   6,   1 ]
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A130469, A007489, A000142, A055790, A047920, A068106, A130470, A130471.

Cf. A182961.

Programs

Magma

m:=21; [ &+([ k*Factorial(j-k): k in [1..j-1] ] cat [ 1 ]): j in [1..m] ]; // Klaus Brockhaus, May 28 2007

Extensions

Edited and extended by Klaus Brockhaus, May 28 2007